A satellite orbits a planet of mass M in a circular orbit of radius r (measured from the planet's center). What are the orbital speed v and orbital period T?

Question

Accepted Answer

v = \sqrt{GM/r}, T = 2\pi\sqrt{r^3/(GM)}

Setting gravity equal to centripetal force: GM m/r^2 = m v^2/r, so v = \sqrt{GM/r}. Then T = 2\pi r/v = 2\pi\sqrt{r^3/(GM)} (Kepler's third law).

Answer

v = \sqrt{GM/r}, T = 2\pi\sqrt{r^3/(GM)}

Answer

v = GM/r, T = 2\pi r/\sqrt{GM}

Answer

v = \sqrt{2GM/r}, T = 2\pi r^2/(GM)

Answer

v = \sqrt{GM r}, T = 2\pi r/v

Motion of Orbiting Satellites

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